With margins and their uncertainties, QMU (Quantification of Margin and Uncertainty) method can be used to make decisions on whether performances of a product reach demands or not. Recur to new methods of UQ (Uncertainty Quantification) for M&S (Modeling & Simulation), QMU is actualized with input information directly from M&S and its uncertainties. With reliability assessment for a stockpiled product, main ideas and executing details of QMU decision are demonstrated.

An approach for numerically solving nonlinear diffusion equations on 2D scattered point distributions is developed with finite directional difference method. The approach yields stencils of minimal size using five neighboring points. And coefficients of discretization have explicit expressions. A scheme employing five-point formulae is proposed to discretize multimedia interface condition for discontinuous problems in which approximation to flux on interface is second-order accurate. The discretization methods show good performance in numerical examples with different computational domains and different point distributions.

A class of meshfree methods——finite point method on a set of two-dimensional disordered points is studied. Fundamentals of the method are established by means of directional differentials and directional differences. Formulae relating to multi-directional differentials of each order are given. Based on these formulae and with different numbers of neighboring points, five-peint formulae and less-point (two-point, three-point and four-point) formulae are derived, respectively. Solvability conditions of the five-point formulae and permissible set of neighboring points are discussed. Approximate expressions for classical differential operators on a set of disordered points are derived. It is demonstrated with theoretical analysis and numerical experiments that the accuracy of these formulae is improved as the number of neighboring points increases. These approximate formulae lay foundation for constructing computational schemes of partial differential equations on a set of disordered points. They can be applied to computational methods on unstructured meshes to increase accuracy as well.